You are babysitting for 3 hours. You will receive $12. What is your hourly wage?

● Underline the numbers and units you need to solve the problem.

● Write each important number or word, with its units, on a piece of paper. Make fi ve other pieces of paper with +, −, ×, ÷, and =.

● Arrange the pieces of paper to form an equation. Use it to answer the key word question “What is your hourly wage?”

Make sure the units for the key word are the same as the units in the expression.

● Evaluate the expression on the right side of the equation.

Hourly wage = 12 ÷ 3 Write.

= 4 Evaluate.

So, your hourly wage is $4 per hour.

EXAMPLE: Reading and Re-Reading1

Evaluating Algebraic Expressions1.1

2 Chapter 1 Expressions and Number Properties

How can you write and evaluate an expression

that represents a real-life problem?

You are babysitting for 3 hours. You will receive $12.What is your hourly wage?

3 h hourly wage ($ per hour)

$12+ =

÷×

3 h $12 ÷=

Write the problem. Underline the important numbers and units.

Read the problem carefully a second time. Underline the key word for the question.

dollars per hour dollars per hour

hourly wage ($ per hour)

Section 1.1 Evaluating Algebraic Expressions 3

Use what you learned about evaluating expressions to complete Exercises 4 –7 on page 6.

Work with a partner. Use the strategy shown in Example 1 to write an expression for each problem. After you have written the expression, evaluate it using mental math or some other method.

a. You are washing cars for 2 hours. You will receive $6. How much will you earn per hour?

b. You have $60. You buy a pair of jeans and a shirt. The pair of jeans costs $27. You come home with $15. How much did you spend on the shirt?

c. For lunch, you buy 5 sandwiches that cost $3 each. How much do you spend?

d. You are running a 4500-foot race. How much farther do you have left to go after running 2000 feet?

e. A young rattlesnake grows at a rate of about 20 centimeters per year. How much does a young rattlesnake grow in 2 years?

ACTIVITY: Reading and Re-Reading22

3. IN YOUR OWN WORDS How can you write and evaluate an expression that represents a real-life problem? Give one example with addition, one with subtraction, one with multiplication, and one with division.

Lesson1.1

4 Chapter 1 Expressions and Number Properties

Study TipYou can write the product of 4 and n in several ways. 4 ⋅ n 4n 4(n)

Key Vocabularynumerical expression, p. 4algebraic expression, p. 4evaluate, p. 4

A numerical expression contains only numbers and operations. An algebraic expression may contain numbers, operations, and one or more variables. Here are some examples.

Numerical Expression Algebraic Expression

15 + 9 ⋅ 3 45 ÷ p − q

To evaluate an algebraic expression, substitute a number for each variable. Then use the order of operations to fi nd the value of the numerical expression.

a. Evaluate k + 10 when k = 25.

k + 10 = 25 + 10

= 35 Add 25 and 10.

b. Evaluate 4 ⋅ n when n = 12.

4 ⋅ n = 4 ⋅ 12

= 48 Multiply 4 and 12.

1. Evaluate 24 + c when c = 9. 2. Evaluate d − 17 when d = 30.

EXAMPLE Evaluating Algebraic Expressions11

Substitute 25 for k.

Substitute 12 for n.

Evaluate a ÷ b when a = 27 and b = 3.

a ÷ b = 27 ÷ 3

= 9 Divide 27 by 3.

Evaluate the expression when p = 24 and q = 8.

3. p ÷ q 4. q + p 5. p − q 6. pq

EXAMPLE Evaluating an Expression with Two Variables22

Substitute 27 for a.

Substitute 3 for b.

Exercises 8 –19

Lesson Tutorials

Section 1.1 Evaluating Algebraic Expressions 5

a. Evaluate 3x − 14 when x = 5.

3x − 14 = 3(5) − 14 Substitute 5 for x.

= 15 − 14 Using order of operations, multiply 3 and 5.

= 1 Subtract 14 from 15.

b. Evaluate z 2 + 8.5 when z = 2.

z 2 + 8.5 = (2)2 + 8.5 Substitute 2 for z.

= 4 + 8.5 Using order of operations, evalute 22.

= 12.5 Add 4 and 8.5.

Evaluate the expression when y = 6.

7. 5y + 1 8. 30 − 24 ÷ y 9. y 2 − 7 10. 1.5 + y 2

EXAMPLE Evaluating Expressions with Two Operations33

Your aunt gives you $45 to start and you save $3 each week. The expression 45 + 3w gives the amount of money you save after w weeks.

a. How much will you have after 4 weeks, 10 weeks, and 20 weeks?

b. After 20 weeks, can you buy the skateboard? Explain.

a.

b. After 20 weeks, you have $105. So, you cannot buy the $125 skateboard.

11. WHAT IF? In Example 4, the expression for how much money you have after w weeks is 45 + 4w. Can you buy the skateboard after 20 weeks? Explain.

EXAMPLE Real-Life Application44

Number of Weeks, w

45 + 3w Amount Saved

4 45 + 3(4) 45 + 12 = $57

10 45 + 3(10) 45 + 30 = $75

20 45 + 3(20) 45 + 60 = $105

Exercises 25–33

Substitute the given number of weeks for w.

9+(-6)=3

3+(-3)=

4+(-9)=

9+(-1)=

6 Chapter 1 Expressions and Number Properties

Exercises1.1

1. VOCABULARY Copy and complete the table.

2. NUMBER SENSE Which step in the order of operations is fi rst? second? third? fourth?

3. NUMBER SENSE Will the expression 20 − x get larger, smaller, or stay the same as x gets larger? Explain.

Write and evaluate an expression for the problem.

4. You receive $8 for raking leaves for 2 hours. What is your hourly wage?

5. Music lessons cost $20 per week. How much do 6 weeks of lessons cost?

6. The scores on your fi rst two history tests were 82 and 95. By how many points did you improve on your second test?

7. You buy a hat for $12 and give the cashier a $20 bill. How much change do you receive?

ALGEBRA Evaluate the expression when a = 3, b = 2, and c = 12.

8. 6 + a 9. b ⋅ 5 10. c − 1 11. 27 ÷ a

12. 12 − b 13. c + 5 14. 2a 15. c ÷ 6

16. a + b 17. c − a 18. c —

a 19. b ⋅ c

20. ERROR ANALYSIS Describe and correct the error in evaluating the expression when m = 8.

21. LAWNS You earn 15n dollars for mowing n lawns. How much do you earn for mowing one lawn? seven lawns?

Add and subtract from left to right. Multiply and divide from left to right.

Evaluate powers. Evaluate expressions inside grouping symbols.

Algebraic Expression Numbers Variables Operations

x − 8 8 x Subtraction

3w + 9

6y − 12

Sample

5m + 3 = 5 ⋅ 8 + 3 = 5 ⋅ 11 = 55

✗

11 22

Help with Homework

Section 1.1 Evaluating Algebraic Expressions 7

22. FINGERNAIL After m months, the length of a fi ngernail is 10 + 3m millimeters. How long is the fi ngernail after eight months? three years?

Copy and complete the table.

23. x 3 6 9

x ⋅ 8

24. x 2 4 8

64 ÷ x

ALGEBRA Evaluate the expression when a = 10, b = 9, and c = 4.

25. 2a + 3 26. 4c − 7.8 27. a

— 2

+ 1

28. 27

— b

+ 8 29. c 2 + 6 30. a 2 − 18

31. a + 9c 32. bc + 12.3 33. 3a + 2b − 6c

34. QUILT You are bordering a quilt with a blue ribbon. Which expression tells you how much ribbon you will need? Draw a diagram to help explain your reasoning.

2(w + 72) 2w + 72

35. DECK Your deck has an area of 128 square feet. After adding a section, the area will be s 2 + 128 square feet. Draw a diagram of how this can happen.

36. SCIENCE CENTER The expression 20a + 13c is the cost for a adults and Adults: $20Students: $13Adults: $20Students: $13

c students to enter the Science Center.

a. Find the total cost for 4 adults and 24 students.

b. You fi nd the cost for a group. Then the numbers of adults and students in the group both double. Does the cost double? Explain your answer using an example.

c. In part (a), the number of adults doubles, but the number of students is cut in half. Is the cost the same? Explain your answer using an example.

Plot the points in a coordinate plane. (Skills Review Handbook)

37. (3, 2) 38. (2, 3) 39. (5, 1) 40. (1, 8)

41. MULTIPLE CHOICE Which numbers have a least common multiple of 24? (Skills Review Handbook)

○A 4, 6 ○B 2, 22 ○C 3, 8 ○D 6, 12

33

72 in.

w in.